oapackage-package: Orthogonal Array Package

Description Details Author(s) References See Also Examples

Description

This package creates 2-level D-optimal designs with a user specified optimization function.

A design with non-zero D-efficiency can be used to estimate a model with all the main effects and all the two-factor interactions. The effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two-factor interactions. The optimization functions in this package allow to user to create D-optimal designs that favor the main effect estimation over the estimation of two-factor interactions.

Details

The main function in the package is Doptimize. This function generates a single D-optimal design. The optimization function is specified using three parameters α_1, α_2, α_3. The following function is then optimized:

F = α_1 D + α_2 Ds + α_3 D1

Here D is the D-efficiency of the design. The Ds- and D1-efficiency are defined further below.

When specifying alpha_1=1, alpha_2=alpha_3=0 the function generates design that optimizes the D-efficiency. For values of alpha_2>0 the main effects are given more weight. This allows the user to create designs with good estimation of the main effects, while still allowing to estimate all 2-factor interactions.

The Ds- and D1-efficiency are defined as follows. For a design D the model matrix X can be split into [I X_1 X_2] with I the intercept, X_1 the main effects and X_2 the second order effects. We let X_{02}=[I X_2] and define D1=(|X_1^T X_1|)^{1/(k+1)}, Ds=(|X^T X|/|X_{02}^T X_{02} |)^{1/k} with k the number of factors of the design.

More details of the method and results of the the generation of optimal designs can be found the paper Eendebak (2015).

Author(s)

P.T. Eendebak <pieter.eendebak@gmail.com>

Alan Vazquez

References

Eendebak, P.T. and Schoen, E.D. (2015) Two-level designs to estimate all main effects and two-factor interactions, submitted to Technometrics

See Also

The documententation for Doptimize and Defficiencies.

For example code see the file example_Doptimize.R or example_design_usage.R included in the tests of the package.

Examples

1
p = Doptimize(N=32, k=7, nrestarts=20, alpha1=1, alpha2=1, alpha3=0)

Example output

Doptimize: iteration 0/20
Doptimize: iteration 19/20
Doptimize: generated design with D = 0.846190, Ds = 0.891215

oapackage documentation built on May 29, 2017, 11:03 p.m.